Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $10. Each consumer will buy at most 1 unit, and will buy it from whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by ci(qi) = 4qi . Because of governmental regulation, firms can only choose prices which are multiples of $0.25, and they cannot price above $10. This game has 3 Nash equilibria in pure strategies. Find them all.

Note to tutor: I have heard that the 3 pure strategy nash equilibria are:

(4,4)

(4.25,4.25)

(4.5,4.5)